Can someone please help me with this question. Please explain how they got these answers!! I am confused!! Thank you so much!!

Herzog Industries sells two electrical components with the following characteristics. Fixed costs for the company are $420,000 per year. XL-709 CD-918 Sales Price $18 $33 Variable cost $14 $25 Sales Volume 84,000 units 126,000 units

(a). How many units of each product must Herzog Industries sell in order to break even for XL-709 and CD-918?

Answer given: Break even units 26,250 for XL-709 39,375 for CD-918

How did they arrive at the answer for the Sales mix?? I cant figure it out!! Their answer is showing as 8.40:12.60 or 1:1.5

The solution given is:

($18 - $14)x + ($33 - $25)(1.5x) - $420,000 = $0 $4x + 8 (1.5x) = $420,000 16x = $420,000 QUESTION: How did they get 16x???

x = 26,250 XL-709 x = 39,375 CD-918

(b). Herzogs Vice President of Sales has determined that due to market changes, the sales price of component XL-709 can be increased to $22 with no impact on sales volume. What will be Herzogs new breakeven point in units?

Answer given: New Break even point in units 21,000 for XL-709 31,500 for CD-918

The solution given is:

New XL-709 contribution margin: $22 - $14 = $8 Let x = number of XL-709s sold ($22 - $14)x + ($33 - $25)(1.5x) - $420,000 = $0 $8x = 8 (1.5x) = $420,000 $20 x = $420,000 QUESTION: How did they get $20???

X = 21,000 XL-709s

1.5x = 31,500 CD-918s

(c ). Returning to the original information, Herzogs vice president of marketing believes that spending $126,000 on a new advertising campaign will increase sales of component CD-918 to 168,000 units, without affecting the sales of product XL-709. How many units of each product must Herzog sell to break even under this new scenario?

Answer given: Break even units 27,300 for XL-709 54,600 for CD-918

How did they arrive at the answer for the Sales mix?? New sales mix: 8.40:16.80 or 1:2

New fixed expense = $420,000 + 126,000 = $546,000

The solution given is:

Let x = number of XL-709s sold

($18 - $14)x + ($33 - $25)(2x) - $546,000 = $0 $4x + $8 (2x) = $546,000 $20x = $546,000 QUESTION: How did they get 20x???

x = 27,300 XL-709s 2x = 54,600 CD-918s

(d). The market changes referred to in part (b) indicate additional overall demand for component XL-709. Herzogs vice president of marketing believes that if the company spends $126,000 to advertise component XL-709 rather than CD-918, as planned in part (c), the company will be able to sell a total of 105,000 units of XL-709 at the new price of $22. If the company must choose to advertise only one component, which component should receive the additional $126,000 in advertising?

Answer given: The company should advertise product XL-709 since it expects to earn $168,000 more in operating income than if it advertised CD-918

The solution given is:

Let x = number of XL-709s sold

Operating income if the company advertises XL-709: [($22 - $14) x 105,000)] + [($33 - $25) x 126,000)] - $546,000 = $1,302,000 QUESTION: How did they get 105,000?

Operating income if the company advertises CD-918: [($18 - $14) x 84,000)] + [($33 - $25) x 168,000)] - $546,000 = $1,134,000